In a mobile telecommunications network, the period when an MS resides in a cell is called the MS cell residence time. The period between when a call arrives at the MS and when the MS moves out of the cell is called the residual life of the MS cell residence time. In performance evaluation of a mobile network, it is important to derive the residual life distribution from the cell residence times. This distribution determines if a connected call will be handed over to a new cell, and therefore significantly affects the call dropping probability. In mobile network simulation, generating the residual-life random numbers is not a trivial task, which has not been addressed in the literature. This paper shows how to generate the random numbers from the residual life distribution, and develop the residual-life random number generation procedure for cell residence times with the gamma distribution.